Effective pedagogy in mathematics#

Henderson et al (2020) - Improving upper primary and lower secondary#

Offer 8 recommendations. A distillation of research with the intent of providing evidence-based advice for teachers.

Use assessment to build on students' existing knowledge and understanding#

Could be said to be a combination of assessment-for-learning, targeted-teaching, and leveraging knowledge of mathematical-misconceptions

Use manipulatives and representations#

Effective use of enactive-mathematics-pedagogy. Purposeful use and temporary use to act as a scaffold to be removed.

Scaffolding to be removed?

e.g. Boaler in mathematical-mindsets suggests that counting on hands should not be discouraged, but actively encouraged. Her ideas of multiple representations could include use of manipulatives.

Teach strategies for solving problems#

Help students develop and use effectively readily available methods for problem solving in familiar and unfamiliar situations. Suggests use of worked-examples as a way to evaluate methods. Students should be able to engage metacognitively about methods.

Enable students to develop a rich network of mathematical knowledge#

Teach students to use/recognise mathematical structure. Emphasise TIMTOWTDI in mathematics, but also an emphasis on fluent recall of facts, teaching of procedures.

Develop students' independence and motivation#

Students take responsibility and play an active role. Develop metacognition, including teacher modeling. Avoid doing too much too early. "Positive attitudes are important, but there is scant evidence on the most effective ways to foster them

Use tasks and resources to challenge and support students mathematics#

Use stories and problem to help students understand mathematics. Develop conceptual and procedural knowledge. Use technology. Also aspects of the using assessment point above

Use structured interventions to provide additional support#

targeted-teaching

Support students to make a successful transition between primary and secondary#

Address the identified large dip in mathematical attainment.

Anthony and Walshaw (2009) - Effective pedagogy in mathematics#

Propose a collection of principles for effective mathematical pedagogy. Each principle is supported by literature and overall the work is informed by a collection of beliefs.

Beliefs that mathematics pedagogy must#

be grounded in the general premise that all students have the right to access education and the specific premise that all have the right to access mathematical culture;

acknowledge that all students, irrespective of age, can develop positive mathematical identities and become powerful mathematical learners;

be based on interpersonal respect and sensitivity and be responsive to the multiplicity of cultural heritages, thinking processes, and realities typically found in our classrooms;

be focused on optimising a range of desirable academic outcomes that include conceptual understanding, procedural fluency, strategic competence, and adaptive reasoning;

be committed to enhancing a range of social outcomes within the mathematics classroom that will contribute to the holistic development of students for productive citizenship.

Principles#

1. An ethic of care#

Caring classroom communities that are focused on mathematical goals help develop students’ mathematical identities and proficiencies.

2. Arranging for learning#

Effective teachers provide students with opportunities to work both independently and collaboratively to make sense of ideas

3. Building on students' thinking#

Effective teachers plan mathematics learning experiences that enable students to build on their existing proficiencies, interests, and experiences.

4. Worthwhile mathematical tasks#

Effective teachers understand that the tasks and examples they select influence how students come to view, develop, use, and make sense of mathematics.

5. Making connections#

Effective teachers support students in creating connections between different ways of solving problems, between mathematical representations and topics, and between mathematics and everyday experiences.

6. Assessment for learning#

Effective teachers use a range of assessment practices to make students’ thinking visible and to support students’ learning.

7. Mathematical Communication#

Effective teachers are able to facilitate classroom dialogue that is focused on mathematical argumentation.

8. Mathematical language#

Effective teachers shape mathematical language by modelling appropriate terms and communicating their meaning in ways that students understand.

9. Tools and representations#

Effective teachers carefully select tools and representations to provide support for students’ thinking.

10. Teacher knowledge#

Effective teachers develop and use sound knowledge as a basis for initiating learning and responding to the mathematical needs of all their students.

References#

Anthony, G., & Walshaw, M. (2009). Effective Pedagogy in Mathematics. Educational Practices Series-19. In UNESCO International Bureau of Education. UNESCO International Bureau of Education.

Henderson, P., Hodgen, J., Foster, C., Kuchemann, D., Deeble, M., Toon, D., Vaughan, T., & Schoeffel, S. (2020). Improve mathematics in upper primary and lower secondary. Evidence for Learning.